In 1839, he followed his cousin, Cardale, to St John's College, Cambridge and graduated in 1843, seventh in the first class of the classical tripos and a senior optime.
In his lectures, illustrated from his own collections of coins and vases, he dealt chiefly with Greek and Ancient Roman pottery and numismatics.
He also brought out the editio princeps of the speeches of Hypereides Against Demosthenes (1850), On Behalf of Lycophron and Euxenippus (1853) and his Funeral Oration (1858).
It was by his edition of these speeches from the papyri discovered at Thebes (Egypt) in 1847 and 1856 that Babington's fame as a Greek scholar was made.
[3] In 1855, he published an edition of Benefizio della Morte di Cristo, a remarkable book of the Reformation period, attributed to Paleario, of which nearly all the copies had been destroyed by the Inquisition.
Babington's edition was a facsimile of the editio princeps published at Venice in 1543, with an Introduction and French and English versions.